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We examine two conventional approaches to this problem \u2014 simply to ignore unit root problems or to use unit root pretests to determine the critical values for second-stage inference\u2014and show that both exhibit substantial size distortions in empirically plausible situations. We then propose an alternative approach in which the second-stage critical values depend continuously on a first-stage statistic that is informative about the order of integration of the regressor. This procedure has the correct size asymptotically and good local asymptotic power.<\/jats:p>","DOI":"10.1017\/s0266466600008720","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:43:23Z","timestamp":1236699803000},"page":"672-700","source":"Crossref","is-referenced-by-count":141,"title":["Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown"],"prefix":"10.1017","volume":"10","author":[{"given":"Graham","family":"Elliott","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James H.","family":"Stock","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600008720_ref024","doi-asserted-by":"publisher","DOI":"10.2307\/2297602"},{"key":"S0266466600008720_ref025","volume-title":"Time Series Modeling with a Bayesian Frame of Reference: I. 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